A circle is inscribed in △ABC, touching AB, BC, and AC at the points P, Q, and R, respectively. IF AB -BC = 4cm, AB - AC = 2cm and the perimeter of △ABC = 32 cm, then BC/2 (in cm)=?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 13/3
AB - BC = 4 .....(1
AB - AC = 2 .....(2
Perimeter of ΔABC = 32
AB + BC + AC + = 32 .....(3
Adding equations (1, (2, and (3 -
3AB = 32 + 4 + 2
3AB = 38
AB = 38/3
AB - BC = 4
38/3 - BC = 4
BC = (38 - 12)/3
BC = 26/3
BC/2 = 26/6 = 13/3